Conventional image noise removal (or reduction) algorithms may be divided into two categories: statistical methods and kernel methods. One statistical method algorithm is median filtering. In median filtering, a value for a respective pixel in a set of (noisy) pixels to be cleaned up in an image is determined as a median pixel value in a specified window centered at the respective pixel. While Median filtering may be effective in removing or reducing impulse noise, it often has difficulty in removing Gaussian (white) noise and may blur the image (i.e., the image may be smoothed). Blurring may be more pronounced when the window is larger, for example, in images with a high percentage of impulse noise.
Another statistical method, order-statistics (OS) filtering may offer a reduced amount or degree of blurring. In OS filtering, the set of pixels in the window are arranged as an ordered sequence and the respective pixel is replaced by a linear combination of this sequence using suitable pre-determined weights. However, the same window (shape and size) and the same weights may be used for each pixel in the image. As a consequence, it is often difficult to preserve or maintain an overall image sharpness.
Kernel methods, such as moving average (MA) filtering, infinite impulse response (IIR) or autoregressive moving average (ARMA) filtering (i.e., MA in conjunction with autoregressive feedback), and convolution filtering, may be more effective in reducing Gaussian noise, but may be less effective in reducing impulse noise. In addition, depending on filter coefficients (also referred to as filter weights), kernel methods may have even more difficulty than the statistical methods in preserving image sharpness.
Conventional image filtering, including the statistical and the kernel methods, often achieve noise reduction by image smoothing, and thus, by sacrificing image sharpness. This may lead to excessive blurring of the image. While there have been attempts to modify these methods to preserve a certain amount of image sharpness (for example, through the use of a convolution mask for each pixel in accordance with an inverse gradient), such approaches entail increased computational cost and complexity, and often use multi-stage processing (i.e., numerous iterations of the image processing) of the image.
Recent advances in image noise removal include the “maximum a posteriori” (MAP) and variational approaches. The MAP approach is statistical (i.e., discrete) in nature. The variational approach is analytical and is often proposed as a minimization problem of an energy functional, which is often defined as a summation of a bending or internal (“a prior”) energy functional. While the internal energy functional governs the output image quality, the external energy functional measures the proximity to the input image to be cleaned up. A positive constant is used as a parameter for balancing image (smoothness/sharpness) quality and fidelity of the output “clean” image in comparison with the input noisy image (governed by the external energy). The steepest decent approach to solving the Euler-Lagrange equation of the energy minimization problem gives rise to the (isotropic and anisotropic) diffusion and diffusion-reaction partial differential equations (PDE). While the variational approach and other recent related approaches (such as numerical solutions of an anisotropic diffusion or diffusion-reaction PDE) usually provide an improvement over the conventional algorithms discussed above, the improvement often entails increased computational cost and complexity, and often uses multi-stage processing of the image.
There is a need, therefore, for an improved image processing approach that removes or reduces noise in an image while substantially preserving image content (such as image texture and image edges). There is also a need for reduced computational cost, reduced complexity and one-pass or a reduced number of stages in processing of images.